Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON):

Solution:


n = int(raw_input())

#generate a bunch of triangle numbers up to n
storage = [] #stores triangle numbers 
i = 1
currentTotal = 0
while currentTotal < n:
	#generate
	currentTotal = i*(i+1)/2
	storage.append(currentTotal)
	i += 1


#loop ends, we are left with a list of sorted triangle numbers
i = 0
j = len(storage) - 1
found = 0
while i <= j:
	sum1 = storage[i] + storage[j]
	if sum1 == n:
		found = 1
		break
	elif sum1 > n:
		j = j-1
	else:
		i = i+1

if found == 1:
	print "YES"
else:
	print "NO"